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(a + b)2 = a2 + 2ab + b2

Question 1 :

Expand (5x + 3)²

Solution:

Here the given question is in the form of (a+b)². Instead of a we have "5x" and instead of b we have "3" .

So we need to apply the formula a² + 2ab + b² and we need to apply those values of a and b

a = 5 x and b = 3

(5x + 3)² = (5x)² + 2 (5x) (3) + (3)²

= 25x² + 30 x + 9

= 25x² + 30 x + 9

Question 2 :

Expand (x + 2) ²

Solution:

Here the question is in the form of (a+b) ². Instead of a we have "x" and instead of b we have "2".

So we need to apply the formula a² + 2ab + b ² and we need to apply those values of a and b

a = x and b = 2

(x + 2)² = (x)² + 2 (x) (2) + (2)²

= x² + 4 x + 4

Question 3 :

If a + b = 3 and a² + b² = 29,find the value of ab.

Solution:

In this problem to get the value of ab we can use the formula for a plus b whole square that is (a + b)² = a² + b² - 2 a b

3² = 29 - 2ab

9 = 29 - 2 ab

2 a b = 29 - 9

2 a b = 20

ab = 20/2

ab = 10

Question 4 :

[√2 + (1/√ 2)]² is equal to

Solution:

(a + b)² = a² + b² + 2 a b

a = √2 b = 1/√2

[√2 + (1/√ 2)]² = ( √2 )² + (1/√2)² + 2 √2 (1/√2)

= 2 + (1/2) + 2

= 4 + (1/2)

= 9/2

Question 5 :

(105)² is equal to

Solution:

Instead of multiplying 105 x 105 to get the value of (105)² we can use algebraic formula for a plus b whole square that is (a+b)² to get the same answer.105 can be written as 100 + 5.

(105)² = (100 + 5)²

(a + b)² = a² + b² + 2 a b

a = 100 b = 5

(105)² = (100)² + (5)² + 2 (100)(5)

= 10000 + 25 + 1000

= 11025

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